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Math Help - Distance help

  1. #1
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    Distance help

    Can someone help explain how to do this problem?

    Pizza Delivery Problem
    : Ida Livermore starts off on her route. She records her truck's speed, v(t), in mi/hr, at various times, t, in seconds, since she started.

    v(t)=5t^()


    Approximately how far did Ida's truck travel from t=1 to t=9?
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  2. #2
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    What do you know about these three guys?

    s(t) - Position
    v(t) - Velocity
    a(t) - Acceleration

    ????

    That is their usual names, anyway.

    Derivative move down the list. Antiderivative move up. Which do you need.
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  3. #3
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    Quote Originally Posted by TKHunny View Post
    What do you know about these three guys?

    s(t) - Position
    v(t) - Velocity
    a(t) - Acceleration

    ????

    That is their usual names, anyway.

    Derivative move down the list. Antiderivative move up. Which do you need.
    Well, I know that you need find the derivative, but I don't understand how to get the answer of 127 feet. (I looked up the answer in the back of my book.)

    **When I did the problem, I got 86.2 for my derivative.
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  4. #4
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    Quote Originally Posted by Cursed View Post
    Well, I know that you need find the derivative, but I don't understand how to get the answer of 127 feet. (I looked up the answer in the back of my book.)

    **When I did the problem, I got 86.2 for my derivative.
    I don't understand why find the derivative.
    It should be integration.

    V(t) is in mi/hr, while t is in seconds. And the book answer is in feet.
    The units don't tally.

    Convert mi/hr into ft/sec.
    (1mi/1hr)(5280ft/1mi)(1hr/3600sec) = (5280)/(3600) = 1.4667 ft/sec

    So the
    V(t) in mph = 5*t^(1/2)
    should be
    V(t) in ft/sec = (5*1.4667)t^(1/2)

    S = (5*1.4667)INT.(1-->9)[t^(1/2)]dt
    S = (7.333)(2/3)[t^(3/2)]|(1-->9)
    S = (4.888)[9^(3/2) -1^(3/2)]
    S = (4.888)[27 -1]
    S = 127.088
    or
    S = 127 ft.
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